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This paper develops a heuristic algorithm for solving a routing and scheduling problem for tramp shipping with discretized time windows. The problem consists of determining the set of cargoes that should be served by each ship, the arrival, departure, and waiting times at each port, while minimizing total costs. The heuristic proposed is based on a variable neighborhood search, considering a number of neighborhood structures to find a solution to the problem. We present computational results, and, for comparison purposes, we consider instances that can be solved directly by CPLEX to test the performance of the proposed heuristic. The heuristics achieves good solution quality with reasonable computational times. Our computational results are encouraging and establish that our heuristic can be utilized to solve large real-size instances.

A Heuristic Procedure for a Ship Routing and Scheduling Problem with Variable Speed and Discretized Time Windows